Multivariate Phylogenetic Comparative Methods: Evaluations, Comparisons, and Recommendations
Recent years have seen increased interest in phylogenetic comparative analyses of multivariate data sets, but to date the varied proposed approaches have not been extensively examined. Here we review the mathematical properties required of any multivariate method, and specifically evaluate existing...
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Veröffentlicht in: | Systematic biology 2018-01, Vol.67 (1), p.14-31 |
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description | Recent years have seen increased interest in phylogenetic comparative analyses of multivariate data sets, but to date the varied proposed approaches have not been extensively examined. Here we review the mathematical properties required of any multivariate method, and specifically evaluate existing multivariate phylogenetic comparative methods in this context. Phylogenetic comparative methods based on the full multivariate likelihood are robust to levels of covariation among trait dimensions and are insensitive to the orientation of the data set, but display increasing model misspecification as the number of trait dimensions increases. This is because the expected evolutionary covariance matrix (V) used in the likelihood calculations becomes more ill-conditioned as trait dimensionality increases, and as evolutionary models become more complex. Thus, these approaches are only appropriate for data sets with few traits and many species. Methods that summarize patterns across trait dimensions treated separately (e.g., SURFACE) incorrectly assume independence among trait dimensions, resulting in nearly a 100% model misspecification rate. Methods using pairwise composite likelihood are highly sensitive to levels of trait covariation, the orientation of the data set, and the number of trait dimensions. The consequences of these debilitating deficiencies are that a user can arrive at differing statistical conclusions, and therefore biological inferences, simply from a dataspace rotation, like principal component analysis. By contrast, algebraic generalizations of the standard phylogenetic comparative toolkit that use the trace of covariance matrices are insensitive to levels of trait covariation, the number of trait dimensions, and the orientation of the data set. Further, when appropriate permutation tests are used, these approaches display acceptable Type I error and statistical power. We conclude that methods summarizing information across trait dimensions, as well as pairwise composite likelihood methods should be avoided, whereas algebraic generalizations of the phylogenetic comparative toolkit provide a useful means of assessing macroevolutionary patterns in multivariate data. Finally, we discuss areas in which multivariate phylogenetic comparative methods are still in need of future development; namely highly multivariate Ornstein–Uhlenbeck models and approaches for multivariate evolutionary model comparisons. |
doi_str_mv | 10.1093/sysbio/syx055 |
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Here we review the mathematical properties required of any multivariate method, and specifically evaluate existing multivariate phylogenetic comparative methods in this context. Phylogenetic comparative methods based on the full multivariate likelihood are robust to levels of covariation among trait dimensions and are insensitive to the orientation of the data set, but display increasing model misspecification as the number of trait dimensions increases. This is because the expected evolutionary covariance matrix (V) used in the likelihood calculations becomes more ill-conditioned as trait dimensionality increases, and as evolutionary models become more complex. Thus, these approaches are only appropriate for data sets with few traits and many species. Methods that summarize patterns across trait dimensions treated separately (e.g., SURFACE) incorrectly assume independence among trait dimensions, resulting in nearly a 100% model misspecification rate. Methods using pairwise composite likelihood are highly sensitive to levels of trait covariation, the orientation of the data set, and the number of trait dimensions. The consequences of these debilitating deficiencies are that a user can arrive at differing statistical conclusions, and therefore biological inferences, simply from a dataspace rotation, like principal component analysis. By contrast, algebraic generalizations of the standard phylogenetic comparative toolkit that use the trace of covariance matrices are insensitive to levels of trait covariation, the number of trait dimensions, and the orientation of the data set. Further, when appropriate permutation tests are used, these approaches display acceptable Type I error and statistical power. We conclude that methods summarizing information across trait dimensions, as well as pairwise composite likelihood methods should be avoided, whereas algebraic generalizations of the phylogenetic comparative toolkit provide a useful means of assessing macroevolutionary patterns in multivariate data. Finally, we discuss areas in which multivariate phylogenetic comparative methods are still in need of future development; namely highly multivariate Ornstein–Uhlenbeck models and approaches for multivariate evolutionary model comparisons.</description><identifier>ISSN: 1063-5157</identifier><identifier>EISSN: 1076-836X</identifier><identifier>DOI: 10.1093/sysbio/syx055</identifier><identifier>PMID: 28633306</identifier><language>eng</language><publisher>England: Oxford University Press</publisher><subject>Classification ; Comparative analysis ; Computer Simulation ; Data processing ; Datasets ; Evolution ; Mathematical models ; Mathematics ; Matrix ; Models, Biological ; Multivariate Analysis ; Phylogenetics ; Phylogeny ; Principal components analysis ; REGULAR ARTICLES ; Statistics</subject><ispartof>Systematic biology, 2018-01, Vol.67 (1), p.14-31</ispartof><rights>The Author(s) 2017</rights><rights>The Author(s) 2017. Published by Oxford University Press on behalf of the Systematic Biology. All rights reserved. For Permissions, please email: journals.permissions@oup.com 2017</rights><rights>The Author(s) 2017. Published by Oxford University Press on behalf of the Systematic Biology. All rights reserved. For Permissions, please email: journals.permissions@oup.com.</rights><rights>Copyright Oxford University Press, UK Jan 2018</rights><lds50>peer_reviewed</lds50><oa>free_for_read</oa><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c481t-3db6a412a3b169d1a242740f0dd18bd1d7b8f74433e5375c42d957659d5030e83</citedby><cites>FETCH-LOGICAL-c481t-3db6a412a3b169d1a242740f0dd18bd1d7b8f74433e5375c42d957659d5030e83</cites></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktopdf>$$Uhttps://www.jstor.org/stable/pdf/26581915$$EPDF$$P50$$Gjstor$$H</linktopdf><linktohtml>$$Uhttps://www.jstor.org/stable/26581915$$EHTML$$P50$$Gjstor$$H</linktohtml><link.rule.ids>314,780,784,803,1584,27924,27925,58017,58250</link.rule.ids><backlink>$$Uhttps://www.ncbi.nlm.nih.gov/pubmed/28633306$$D View this record in MEDLINE/PubMed$$Hfree_for_read</backlink></links><search><creatorcontrib>Adams, Dean C.</creatorcontrib><creatorcontrib>Collyer, Michael L.</creatorcontrib><title>Multivariate Phylogenetic Comparative Methods: Evaluations, Comparisons, and Recommendations</title><title>Systematic biology</title><addtitle>Syst Biol</addtitle><description>Recent years have seen increased interest in phylogenetic comparative analyses of multivariate data sets, but to date the varied proposed approaches have not been extensively examined. Here we review the mathematical properties required of any multivariate method, and specifically evaluate existing multivariate phylogenetic comparative methods in this context. Phylogenetic comparative methods based on the full multivariate likelihood are robust to levels of covariation among trait dimensions and are insensitive to the orientation of the data set, but display increasing model misspecification as the number of trait dimensions increases. This is because the expected evolutionary covariance matrix (V) used in the likelihood calculations becomes more ill-conditioned as trait dimensionality increases, and as evolutionary models become more complex. Thus, these approaches are only appropriate for data sets with few traits and many species. Methods that summarize patterns across trait dimensions treated separately (e.g., SURFACE) incorrectly assume independence among trait dimensions, resulting in nearly a 100% model misspecification rate. Methods using pairwise composite likelihood are highly sensitive to levels of trait covariation, the orientation of the data set, and the number of trait dimensions. The consequences of these debilitating deficiencies are that a user can arrive at differing statistical conclusions, and therefore biological inferences, simply from a dataspace rotation, like principal component analysis. By contrast, algebraic generalizations of the standard phylogenetic comparative toolkit that use the trace of covariance matrices are insensitive to levels of trait covariation, the number of trait dimensions, and the orientation of the data set. Further, when appropriate permutation tests are used, these approaches display acceptable Type I error and statistical power. We conclude that methods summarizing information across trait dimensions, as well as pairwise composite likelihood methods should be avoided, whereas algebraic generalizations of the phylogenetic comparative toolkit provide a useful means of assessing macroevolutionary patterns in multivariate data. Finally, we discuss areas in which multivariate phylogenetic comparative methods are still in need of future development; namely highly multivariate Ornstein–Uhlenbeck models and approaches for multivariate evolutionary model comparisons.</description><subject>Classification</subject><subject>Comparative analysis</subject><subject>Computer Simulation</subject><subject>Data processing</subject><subject>Datasets</subject><subject>Evolution</subject><subject>Mathematical models</subject><subject>Mathematics</subject><subject>Matrix</subject><subject>Models, Biological</subject><subject>Multivariate Analysis</subject><subject>Phylogenetics</subject><subject>Phylogeny</subject><subject>Principal components analysis</subject><subject>REGULAR ARTICLES</subject><subject>Statistics</subject><issn>1063-5157</issn><issn>1076-836X</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2018</creationdate><recordtype>article</recordtype><sourceid>EIF</sourceid><recordid>eNqFkM9LwzAUx4Mobk6PHpWBFy_VvKRJ2qMUf8GGHhS8lbRJXUe71CQV99-b0enAi6f34H348n0fhE4BXwFO6bVbu6I2YXxhxvbQGLDgUUL52_5m5zRiwMQIHTm3xBiAMzhEI5JwSinmYxTN-8bXn9LW0uvp82LdmHe90r4up5lpO2lluOrpXPuFUe4YHVSycfpkOyfo9e72JXuIZk_3j9nNLCrjBHxEVcFlDETSAniqQJKYiBhXWClICgVKFEkl4phSzahgZUxUygRnqWKYYp3QCboccjtrPnrtfN7WrtRNI1fa9C6HFAikjHMI6MUfdGl6uwrtApUSwonAIlDRQJXWOGd1lXe2bqVd54Dzjcd88JgPHgN_vk3ti1arX_pH3K6h6bt_s84GdOm8sbsozpLwB6PfI4qGJg</recordid><startdate>20180101</startdate><enddate>20180101</enddate><creator>Adams, Dean C.</creator><creator>Collyer, Michael L.</creator><general>Oxford University Press</general><scope>CGR</scope><scope>CUY</scope><scope>CVF</scope><scope>ECM</scope><scope>EIF</scope><scope>NPM</scope><scope>AAYXX</scope><scope>CITATION</scope><scope>K9.</scope><scope>7X8</scope></search><sort><creationdate>20180101</creationdate><title>Multivariate Phylogenetic Comparative Methods</title><author>Adams, Dean C. ; Collyer, Michael L.</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c481t-3db6a412a3b169d1a242740f0dd18bd1d7b8f74433e5375c42d957659d5030e83</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2018</creationdate><topic>Classification</topic><topic>Comparative analysis</topic><topic>Computer Simulation</topic><topic>Data processing</topic><topic>Datasets</topic><topic>Evolution</topic><topic>Mathematical models</topic><topic>Mathematics</topic><topic>Matrix</topic><topic>Models, Biological</topic><topic>Multivariate Analysis</topic><topic>Phylogenetics</topic><topic>Phylogeny</topic><topic>Principal components analysis</topic><topic>REGULAR ARTICLES</topic><topic>Statistics</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Adams, Dean C.</creatorcontrib><creatorcontrib>Collyer, Michael L.</creatorcontrib><collection>Medline</collection><collection>MEDLINE</collection><collection>MEDLINE (Ovid)</collection><collection>MEDLINE</collection><collection>MEDLINE</collection><collection>PubMed</collection><collection>CrossRef</collection><collection>ProQuest Health & Medical Complete (Alumni)</collection><collection>MEDLINE - Academic</collection><jtitle>Systematic biology</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Adams, Dean C.</au><au>Collyer, Michael L.</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Multivariate Phylogenetic Comparative Methods: Evaluations, Comparisons, and Recommendations</atitle><jtitle>Systematic biology</jtitle><addtitle>Syst Biol</addtitle><date>2018-01-01</date><risdate>2018</risdate><volume>67</volume><issue>1</issue><spage>14</spage><epage>31</epage><pages>14-31</pages><issn>1063-5157</issn><eissn>1076-836X</eissn><abstract>Recent years have seen increased interest in phylogenetic comparative analyses of multivariate data sets, but to date the varied proposed approaches have not been extensively examined. Here we review the mathematical properties required of any multivariate method, and specifically evaluate existing multivariate phylogenetic comparative methods in this context. Phylogenetic comparative methods based on the full multivariate likelihood are robust to levels of covariation among trait dimensions and are insensitive to the orientation of the data set, but display increasing model misspecification as the number of trait dimensions increases. This is because the expected evolutionary covariance matrix (V) used in the likelihood calculations becomes more ill-conditioned as trait dimensionality increases, and as evolutionary models become more complex. Thus, these approaches are only appropriate for data sets with few traits and many species. Methods that summarize patterns across trait dimensions treated separately (e.g., SURFACE) incorrectly assume independence among trait dimensions, resulting in nearly a 100% model misspecification rate. Methods using pairwise composite likelihood are highly sensitive to levels of trait covariation, the orientation of the data set, and the number of trait dimensions. The consequences of these debilitating deficiencies are that a user can arrive at differing statistical conclusions, and therefore biological inferences, simply from a dataspace rotation, like principal component analysis. By contrast, algebraic generalizations of the standard phylogenetic comparative toolkit that use the trace of covariance matrices are insensitive to levels of trait covariation, the number of trait dimensions, and the orientation of the data set. Further, when appropriate permutation tests are used, these approaches display acceptable Type I error and statistical power. We conclude that methods summarizing information across trait dimensions, as well as pairwise composite likelihood methods should be avoided, whereas algebraic generalizations of the phylogenetic comparative toolkit provide a useful means of assessing macroevolutionary patterns in multivariate data. Finally, we discuss areas in which multivariate phylogenetic comparative methods are still in need of future development; namely highly multivariate Ornstein–Uhlenbeck models and approaches for multivariate evolutionary model comparisons.</abstract><cop>England</cop><pub>Oxford University Press</pub><pmid>28633306</pmid><doi>10.1093/sysbio/syx055</doi><tpages>18</tpages><oa>free_for_read</oa></addata></record> |
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subjects | Classification Comparative analysis Computer Simulation Data processing Datasets Evolution Mathematical models Mathematics Matrix Models, Biological Multivariate Analysis Phylogenetics Phylogeny Principal components analysis REGULAR ARTICLES Statistics |
title | Multivariate Phylogenetic Comparative Methods: Evaluations, Comparisons, and Recommendations |
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